Step 1: Understanding the Concept:
Nasal congestion is relieved by constricting the blood vessels in the nasal mucosa, and the question asks which drug does this through the \( \alpha_{2} \) adrenergic receptor specifically.
Step 2: Key Formula or Approach:
Separate the options by receptor family: alpha receptors cause vasoconstriction, useful for decongestion, while beta-2 receptors cause smooth muscle relaxation, useful for bronchodilation, and check which option belongs to which family.
Step 3: Detailed Explanation:
Terbutaline and salbutamol are both \( \beta_{2} \) agonists that relax bronchial smooth muscle, which is why they are used as bronchodilators in asthma, not as decongestants.
Methotrexate acts on folate metabolism and has no effect on adrenergic receptors of any kind.
Oxymetazoline activates \( \alpha_{2} \) adrenergic receptors on nasal blood vessels, and this activation constricts the vessels, reducing blood flow and swelling in the nasal mucosa.
That vasoconstriction is exactly what relieves nasal congestion, and it is the mechanism unique to oxymetazoline among the four options.
Step 4: Final Answer:
Oxymetazoline is the \( \alpha_{2} \) agonist used as a nasal decongestant.